This may not be entirely feasible, but I was just curious if it would be possible to use/modify my phone charger or something else that I have to charge my 83+. And hopefully still be able to use the charger for it's actual intended use, too. I saw in SAX that some people have been able to do this...? And I'm wondering how. Hopefully, if it is possible, it won't be too hard.

What are the specs on your phone charger? Is it anything specific or is it a AC->5VDC with USB or similar?

I don't exactly know what that means, but yes, it has a USB that is detachable.

Input: 100-240V~50/60Hz
Output: 5.1v, 700mA

Ok well you have a couple of options, you can power the calc directly via a spliced USB cable ... but it would die when disconnected, or you can look at one of those small 5V Liion/Lipo batteries and chargers to install inside your calc? You can get them for pretty cheap.

Im not sure if a calc will run off 3.7v? Might be worth a test otherwise a small DC-DC converter can be used as well.

A quick ebay:
http://www.ebay.com.au/itm/like/121531508034?limghlpsr=true&hlpv=2&ops=true&viphx=1&hlpht=true&lpid=107&chn=ps

I believe some (maybe all?) 83 plusses will run on 3.7 volts. I'm not sure how safe this is, but mine booted up when I connected a battery to it.

If you would like; you could take a look at this: Mateo's Ultimate Calculator

You can use it to power things and charge your calculator.

Wow, how did you do that? I would especially like to know how you did the USB cable and the wall outlet one. Does it require [permanent?] hardware changes to the calculator? How did you do this? I may not be able to do it to my current calculator, as it is a school rented one, but I would still like to know.

Well, technically no, as long as you keep everything on the case cover. Then you would just need contacts to touch the serial array of batteries. There's some more info later on in the post; any questions you have I can help with!